Differential Calculus on Fuzzy Sphere and Scalar Field

Details Differential Calculus on Fuzzy Sphere and Scalar Field Differential Calculus on Fuzzy Sphere and Scalar Field

1997-10-28

arxiv.org/abs/q-alg/9710034v1

Int.J.Mod.Phys. A13 (1998) 3235-3244

Mathematics

Quantum Algebra

LaTeX 12 pages

Scientific paper

10.1142/S0217751X9800161X

We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.

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